When
you pluck a fixed string, you get reflections and the waves start to
interfere. The result is destructive interference for all frequencies
except those that are harmonics of the fundamental frequency of the
string.

The
harmonics reflect in a way that they are never destroyed but instead
create a complex interaction of standing waves. See
animation.

áHarmonics: series of frequencies that are related by an
integral value

The
fundamental frequency of this interaction is the note we hear or the
pitch.

Pitch:How the human ear perceive
frequency

The
interaction of all the harmonics provide the timbre.

Timbre:
The quality of the sound or fullness of the sound as we hear it.

Solving for Harmonics of a String:

Creates
standing waves with fixed boundaries at each end.

The
fixed ends must be nodes.

All
string instruments work this way.

II. Air Column Open on Both Ends

When
you blow across an open pipe, you get reflections and the waves start to
interfere as they move down the pipe. The result is destructive
interference for all frequencies except those that are harmonics of the
fundamental frequency of the string.

The
harmonics reflect in a way that they are never destroyed but instead
create a complex interaction of standing waves.This is very similar to strings but with a twist. See
animation.

Solving for Harmonics of an Air Column that is open on both
ends:

Creates
standing waves with free boundaries at each end.

The
free ends must be antinodes.

Wind
instruments such as a flute or pipe organ work this way.

III. Air Column Open on one end and closed on one end.

When
waves travel down a tube with a closed end, you get reflections and the
waves start to interfere as they move down the pipe.The result is destructive
interference for all frequencies except those that are harmonics of the
fundamental frequency of the tube.

The
harmonics reflect in a way that they are never destroyed but instead
create a complex interaction of standing waves. This is similar to the
first two but it has a definite difference we will see in the resulting
formula.See
animation.

Solving for Harmonics of an Air Column that has one closed
end and one open end:

Creates
standing waves with free boundary at one end and fixed at the other.

The
free end must be an antinode; the fixed a node.

Wind
instruments such as a trumpet, clarinet work this work this way.

End correction:If you are trying to achieve a certain frequency you need to add an end
correction to the length of pipe you calculate from the above equations.The open end changes things slightly so you
have to add a small amount of length to your calculated value.To find the corrected length, you add 60% of the radius of the air column to the measured length of the pipe.

IV.Beats

áThe perceived difference in volume of two waves that
have frequencies very close to each other.